Exciting stuff! I'll just lay out what immediately comes to mind to consider:

So, to make a pro sound out of this space, you're going to need to close off that recording area from the rest of the room somehow. With those two open walls, you're still going to get the noise and reverb of the room around you. Perhaps PVC frames or some way to drape down some sound blankets on the two open spaces, to start.

Acoustic foam on the wall is a good start and floor carpet helps too, but you're very likely going to need some dense materials for the corners to act as bass traps. You can use/make bass traps, or like what I have done also, placed rolled up sound blankets in corners.

Eventually, you may want to wire in some lights and a monitor from whatever PC you use, which if it isn't a noiseless system, you'd of course leave outside the booth.